Certificate problem with a new machine - credentials supplied to package not recognized

I found the problem and its solution.

The idea is to grant permissions to the account which is used for service identity.

Need to use a tool WinHttpCertCfg.exe. This is helpful for applications using client certificates to get authorization.

It's nicely explained here. http://support.microsoft.com/kb/901183

Thanks to Feroze Daud (http://ferozedaud.blogspot.com/), who answered me on a different forum.